Fundamentals of Engineering Analysis EGR 1302 The Inverse Matrix

Solving Systems of Linear Equations The Inverse Matrix Anxn and Bnxn are Square Matrices of the same Order. A * B = In B * A = In B is called “The Inverse of A” in Algebra, the equivalent is B = A-1 A * A-1 = I

Solving Systems of Linear Equations Sum of Products The same equation can represent any Order.

Solving this System for x1, x2 ( ) ( ) Becomes Subtract

Solving this System for x1, x2 (cont.) factor out the denominator Sum of Products A new Matrix “C”

The Solution to We now have a solution for the Inverse of a 2x2 Matrix

The Determinant The Determinant of A =

Rules for Finding the Inverse of a 2x2 Matrix Rule 1: Swap the Main Diagonal Rule 2: Change Signs on the Back Diagonal Rule 3: Divide by the Determinant

Review of the Solution to a 2x2 System Is solved by If there is no solution Stay Tuned!

A Numerical Example Becomes

Questions?